Method of predicting crop yield loss due to N-deficiency

ABSTRACT

A method for determining the yield loss of a crop using remote sensor data is described. The yield loss is determined using the reflectivity of light by the crop canopy measured from remote sensor data such as an aerial photograph. Pixel color values from the aerial photograph, expressed relative to pixel values from nitrogen-sufficient areas of the field, are transformed to yield losses using a transformation that was developed using empirical data. A similar method is described to determine recommended nitrogen fertilization rates for the crop fields. The yield loss data is useful for nitrogen fertilization management decisions, as it allows a producer of crops to weigh the expense of fertilization against the loss of revenue due to yield loss induced by nitrogen deficiency.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Continuation-in-Part Application ofNon-Provisional application Ser. No. 14/886,712 filed on Oct. 19, 2015,which is a Continuation-in-Part Application of Non-Provisionalapplication Ser. No. 13/959,144 filed on Aug. 5, 2013, now U.S. Pat. No.9,195,891, which is a Continuation-in-Part Application ofNon-Provisional application Ser. No. 13/481,245 filed on May 25, 2012,now U.S. Pat. No. 8,520,891, which is a Divisional Application ofNon-Provisional application Ser. No. 11/936,564 filed on Nov. 7, 2007,now U.S. Pat. No. 8,208,680, which claims priority from ProvisionalApplication Ser. No. 60/857,242 filed on Nov. 7, 2006, all of which arehereby incorporated by reference in their entireties.

FUNDING OF RESEARCH

This work was supported by the U.S. Environmental Protection Agencycontract number X-98756601-0. The U.S. government has certain rights inthis invention.

FIELD

The present invention is directed generally to methods for determiningthe health and yield of a crop, using remote sensing data such as aerialphotographs. In particular, the present invention provides a method ofdetermining optimal nitrogen application rates as well as predictedlosses in crop yield due to nitrogen deficiency.

BACKGROUND

Loss of nitrogen can result in economic loss in crop production systemsdue to nitrogen deficiency and yield limitation. Nitrogen is susceptibleto loss from soils by a variety of mechanisms. The nitrate form ofnitrogen is prone to loss by either leaching or denitrification whensoils are wet. Nitrogen losses associated with wet soil conditions arecommon types of nitrogen loss from agricultural soils. The magnitude ofnitrogen loss, and the process by which the nitrogen is lost, dependsstrongly on soil temperature and soil hydrology. Variations in soiltemperature and hydrology within a field, due to differences inmicroclimate, can lead to substantial spatial variability in the amountof nitrogen that is lost within a given field.

When nitrogen loss occurs after the application of nitrogen fertilizer,a likely outcome, in the absence of any further intervention, is thatthe crop will suffer from nitrogen deficiency, resulting in substantialyield loss and subsequent economic loss. The yields of many crops,including corn, rice, wheat, and potatoes, dramatically increase inresponse to nitrogen applications throughout the vegetative stages ofgrowth.

A traditional approach to avoiding losses in crop yield due to nitrogendeficiency is to apply an excess of nitrogen fertilizer at planting tocompensate for anticipated nitrogen losses due to leaching or othermechanisms. An alternative and arguably more efficient approach to asingle sizable application of nitrogen fertilizer near planting is thepractice of applying a low nitrogen fertilizer rate at planting, whichmay be fully or partially corrected by an additional nitrogenapplication as needed in midseason. A corn producer, for example, mayapply a low nitrogen rate near planting, and then apply additionalnitrogen through a pivot irrigation system at growth stage V9 or later(Ritchie et al. 1993). Because the need for nitrogen is often spatiallyvariable, accurate spatial diagnosis of nitrogen status can reduce theover-application of fertilizer, groundwater contamination, and can alsoincrease nitrogen use efficiency, resulting in reduced operating costs.Thus, applying nitrogen to the growing crop, referred to in the art asrescue nitrogen application, is an effective way to respond to loss offertilizer nitrogen.

Rescue nitrogen applications for corn and other crops are typically moreexpensive than primary nitrogen applications due to the height of thecrops at the time the rescue nitrogen is applied, which usually create aneed for specialized high-clearance equipment or aerial applications ofnitrogen. The availability of equipment for high-clearance or aerialapplications is often limited, meaning that it takes considerable efforton the part of a corn producer to arrange for these nitrogenapplications. Balancing the cost and inconvenience of rescue nitrogenapplication against the economic impact of anticipated yield loss wouldhelp producers to make sound decisions about whether to proceed withrescue nitrogen applications.

Traditional technologies and methods for measuring leaching anddenitrification losses of nitrogen are difficult, expensive, and slow,which limit a producer's ability to predict nitrogen loss and to utilizerescue nitrogen fertilization in order to minimize the potential yieldloss for a particular field or section of a field. The soil may beperiodically tested for nitrogen content at different depths andlocations throughout the fields of a farm. Crop information may also beobtained using an apparatus in which the light with a wavelength relatedto crop nitrogen content is irradiated on a leaf blade of the crop andbased on the reflectivity of the leaf at this wavelength of light; theleaf blade nitrogen content is measured with high precision. However,each of these techniques of monitoring soil and crop nitrogen contentare highly localized. In order to determine the crop informationaccurately for the overall field, as well as to obtain an accuratemapping of the spatial variation of the crop information, numerousrepeats of the minute measurements described above are required.Obtaining crop information in this manner is time-consuming, laborintensive, expensive, and may not supply the information in time for thefarmer to apply rescue nitrogen effectively.

The increasing availability of commercial remote-sensing servicestailored to the needs of agriculture offers new opportunities to developand improve rescue nitrogen management strategies. Several studies haveevaluated remote sensing techniques to determine corn nitrogen statusduring the growing season and have determined that the reflectance ofcorn across all visible and near-infrared wavelengths is correlated withleaf nitrogen concentration or other variables related to crop nitrogenstatus, and therefore can be used to detect nitrogen deficiencies in thecrop canopy. Particularly, nitrogen-deficient corn reflects more visiblelight, and usually less near-infrared light, than nitrogen-sufficientcorn, which suggests that light reflectance can be quantitativelyrelated to the amount of nitrogen stress experienced by the crop.

The specific relationship between crop reflectivity and nitrogen statushas been developed to some extent, but no specific or generalrelationships for predicting nitrogen loss or yield loss from remotelysensed data have been developed. To date, this relationship has beendetermined by adding increasing quantities of nitrogen to a system thatis nitrogen-limited. For application to nitrogen loss situations, it ismore appropriate to define the relationship between color, nitrogenstress, and yield in the context of a fully fertilized crop thatexperiences a range of nitrogen losses. The resulting relationshipbetween nitrogen stress (as measured by crop color) and yield loss mostdirectly addresses the question that is most salient to the producer:does it make good business sense to apply rescue nitrogen fertilizationto my nitrogen-stressed crops, or does the cost of fertilizationoutweigh the gain in crop yield?

Remote sensing using aerial and satellite photography as well as groundbased sensors have been used to determine several parameters related tothe successful cultivation of crops, including soil nutrient content,chlorophyll content of crop leaves, and nitrogen content of crop leaves.The factors measured using remote sensing are correlated with theoverall health and nutrient status of the crops. In general, thesemethods rely on variations in the reflectivity of the soil or the cropcanopy to selected wavelengths of light falling within the visible andthe near-infrared spectrum. Higher crop nitrogen content is associatedwith decreased reflectivity of the leaves in the crop canopy to visiblelight. Although this decreased reflectance of nitrogen-rich plant leavesmay be most pronounced within the green wavelengths of the visible lightspectrum, the reflectance of nitrogen-rich plant leaves in other colorssuch as blue or red may also be significantly correlated to crop health.

Most cameras used for the remote sensing of crops record a three-bandspectral image combining either the near infrared, red, and greenwavelengths or the red, green, and blue wavelengths. Remote sensingmethodologies used for the determination of crop nitrogen statusgenerally process the intensity of the colors contained in each pixel ofa digital image of a field, and determines the variation in theintensity of each color.

Previous methods have used the relative greenness map to makedeterminations about the health of the crops, and in some cases claimthe ability to determine nitrogen fertilization rate. However,optimizing the growth and harvest of the crops is only half of theinformation necessary for a producer to manage the growth and care ofcrops. When managing the production of crops, the producer mustconstantly weigh the cost of additional nitrogen fertilization againstthe potential increase in revenue from the sale of the additional cropyield. To date, current field management methodologies that utilizeremote sensing lack the capability to determine the impact of variationsin the health and nutritional status of crop plants on the crop yield.

At the present time, there exists an unmet need to determine the impactof crop nutrient status on the resulting crop yield using remote sensingtechnology such as aerial photographs. The results of this method wouldmake it possible for the producer to manage the nitrogen supplementationof the crops informed by the economic impact of any nitrogen deficiencyon crop yield.

SUMMARY

The present disclosure provides a method for determining a crop yieldloss due to nitrogen deficiency in at least one or more crop fieldsbased on an analysis of at least one or more remote sensing images. Inthis aspect, the method includes obtaining the one or more remotesensing images of the at least one or more crop fields, represented bypixels or polygons comprised of aggregated pixels, from the at least oneor more remote sensing images. The method also includes selecting acolor from the visible or near-infrared spectrum, or calculating acombination index value comprising at least two selected colors. Areference value for this color or index is selected that representsnitrogen-sufficient plants, either by finding the darkest plants in thefield, the darkest plants in an appropriate neighboring field, or bymeasuring the value in a reference area in which a high rate of nitrogenfertilizer has been applied. In addition, the method includescalculating a relative color or index value of each pixel/polygon in theat least one or more remote sensing images by comparing the color orindex value to the reference color or index value. Most commonly thismay be done by dividing the color or index value by the reference coloror index value, but may also be calculated by subtracting one value fromthe other (FIG. 10), or some other quantitative method of comparison.The relative color or index value is then used to estimate a yield lossof each pixel/polygon from an empirically-derived function of therelative index values (for example, as shown in FIGS. 4, 5, 7, 8, 9, and10). The function used may be linear, polynomial, logarithmic, or someother function that can describe the type of data shown in FIGS. 4, 5,and 7-10 reasonably well.

Further provided herein is a method for determining a nitrogenfertilizer rate to alleviate crop nitrogen deficiency in one or morecrop fields based on an analysis of one or more remote sensing images.The method includes obtaining the one or more remote sensing images ofthe one or more crop fields; calculating a color value for each pixel ofthe one or more remote sensing images or a polygon comprising anaggregation of pixels of the one or more remote sensing images, whereinthe color value is an individual wavelength or a combination index valuecomprising at least two wavelengths; selecting a reference color valuefor the field that represents the color value of crop plants withsufficient nitrogen, to be the same wavelength or combination ofwavelengths; calculating a relative color value of each pixel or polygonin the one or more remote sensing images by quantitatively comparing thecolor value from the pixel or polygon to the reference color value;estimating a nitrogen fertilizer rate of each pixel or polygon from itsrelative color value using an empirically determined mathematicalrelationship between the two quantities; and presenting a summary of allnitrogen rate estimates for the field. The relative color value and thereference value may be quantitatively compared by division, subtraction,or any other method of comparison. The summary of nitrogen rateestimates may be presented visually, as a rate control file, ornumerically with averages, totals, or combinations of the nitrogen rateestimate of each pixel or polygon and may further include a comparisonof the cost of the suggested nitrogen fertilizer treatment with the costof the yield loss. The reference color value may obtained from thedarkest areas in the one or more crop fields being diagnosed or fromcomparable nearby fields, such as the darkest plants in the field, thedarkest plants in an appropriate neighboring field, measuring the valuein a reference area in which a high rate of nitrogen fertilizer has beenapplied, or combinations thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

The inventive method may be employed to predict crop (especially corn)yield loss for nitrogen-deficiency due to low nitrogen fertilizationrate at planting but no nitrogen loss in mid-season(“nitrogen-stress-no-nitrogen-loss”), or due to nitrogen loss caused bywet weather or other factors following sufficient nitrogen fertilizationearly in the season (“nitrogen-loss”).

FIG. 1 is a flowchart illustration of one embodiment of the inventivemethod.

FIG. 2 illustrates the relationship between relative yield and relativegreen from individual fields.

FIG. 3 illustrates the relationship between relative yield and relativegreen from combined data across all seven fields.

FIG. 4 illustrates the relationship between yield loss and relativegreen from individual fields.

FIG. 5 illustrates the relationship between yield loss and relativegreen from combined data across seven fields.

FIG. 6 is a summary of the crop yield resulting from nitrogenfertilization management informed by an assessment of crop nitrogendeficiency using aerial photographic data.

FIG. 7 is a graph summarizing the correlation of crop yield loss as afunction of relative blue value for a plurality of crop fields.

FIG. 8 is a graph summarizing the correlation of crop yield loss as afunction of relative red value for a plurality of crop fields.

FIG. 9 is a graph showing crop yield loss as a function of relativeindex value for a combination index value of infrared and green for aplurality of crop fields, where the relative index value is calculatedby dividing the observed index value by the reference index value.

FIG. 10 is a graph showing crop yield loss as a function of relativered, where relative red is calculated as a difference between theobserved red in an area and the reference red established from thedarkest areas of the field.

FIG. 11 is a graph showing the relationship between relative green,measured from aerial photos, and optimal nitrogen fertilizer ratemeasured across a large group of on-farm fertilizer rate experiments.

FIG. 12 shows an example of using the darkest pixels or polygons toestablish the reference color. Only the darkest pixels or polygons inthe field (bottom) are retained from the original image (top) to use inestablishing the color of the crop with sufficient nitrogen (thereference color).

Corresponding reference characters and labels indicate correspondingelements among the views of the drawings. The headings used in thefigures should not be interpreted to limit the scope of the claims.

DETAILED DESCRIPTION

The present invention describes a method for determining nutrientdeficiency and resulting crop yield loss using aerial photographs andpositional data. In particular, the invention provides a method ofdetermining yield loss due to nitrogen-deficiency using aerialphotographs. In an aspect, the crop may be corn, rice, wheat, potatoes,grass, or cotton. In essence, the invention provides a method forestimating nitrogen deficiency in a field of crops, predicting theresulting loss of crop yield due to the nitrogen deficiency, and lastlyproviding information to help the producer to determine whetheradditional nitrogen fertilization would be economically profitable. Aflowchart showing the steps of one embodiment of the present method isshown in FIG. 1, though some steps may be omitted.

An aerial image or images are obtained of a field or fields of interest,either from an airplane, an unmanned aerial vehicle, a satellite, abuoyant vehicle, or a tower. The aerial image is subdivided intopolygons, which may be individual pixels in the original image oraggregates of pixels. Within each polygon, the color intensity of allpixels is averaged to determine the mean color intensity for the polygonfor a color chosen from red, blue, green, red-edge, near-infrared, or acombination index calculated from two or more of these colors. Thereference color value (C_(ref)) for each field is then determined. Thismay be done by averaging the color intensities of polygons in apre-established area with a high rate of N fertilizer, or by averagingthe color intensities of the darkest polygons among all of the polygonsin that field or a comparable nearby field (FIG. 12). Referring to FIG.12, the wide range of color seen in this field is typical of fieldswhere substantial nitrogen loss has occurred, leaving the areas withwetter soils deficient in nitrogen, resulting in plants with light greenor yellow-green leaves. Partly-fertilized fields may also have a widerange of crop color, and this method can be used in that situation also.When using the darkest polygons in the field, the proportion of allpolygons used in calculating C_(ref) may vary with circumstances, but20% will often be suitable in fully-fertilized fields that have lost Nin wet weather. Once the field's C_(ref) has been established, theRelative Color (RC) values of each pixel or polygon are obtained byquantitatively comparing the value of the color (C_(i)) of each pixel orpolygon to C_(ref). This may be done using division (RC=C_(i)/C_(ref)),subtraction (RC=C_(i)−C_(ref)), or some other method of quantitativelycombining their values. An estimated yield loss is then calculated usinga correlation of yield loss as a function of RC that was predeterminedusing previously measured empirical data. Lastly, the yield loss (YL)values for all polygons in the field are summarized in a meaningful way,which may include one or more of a yield loss map, field average yieldloss, field total yield loss, field total dollar loss, or some othersimple and meaningful summary of yield loss estimates over the wholefield. An economic analysis can then be provided as to whether to addnitrogen to the field or a portion thereof, based on the price of thecrop, the amount of crop lost, and the cost of nitrogen fertilization.

Acquisition and Processing of High Resolution Images of Fields

Remote sensing data may be collected using a variety of instrumentsselected from the list comprising aircraft mounted camera, unmannedaerial vehicle (UAV) mounted camera, helicopter mounted camera,satellite-mounted camera, camera mounted on a tower, and combinationsthereof. In an aspect, the crop may be corn, rice, wheat, potatoes,grass, or cotton. For cornfields, the aerial image of one or more fieldsof interest may be acquired when the crop is between the stages V8 toV18, and more preferably between the stages V10 to V18. Growth stage V8occurs about 4 weeks after the emergence of the corn from the soil; thecorn plant at stage V8 has grown to approximately 50% of its fullheight. Growth stage V18 occurs when the corn plant has grown to itsfull height and just before the plant enters into the reproductivestage.

Optionally, the aerial image may be cropped to include only the one ormore fields of interest with field boundaries and eliminating areas ofhigh soil exposure identified by the operator or using automatedimage-processing rules defined below. In many cases, it is preferable tocrop the image to include only one field, or two adjacent fields, andrepeat as needed to analyze all fields of interest. However, if there isinsufficient information to determine C_(ref) or I_(ref) during imageanalysis, such as the absence of a pre-established reference area, oralternatively a sufficient number of fields lack the minimum number ofnitrogen-sufficient regions to serve as reference areas, then croppingthe image to include multiple fields may be preferable in order toestablish a reliable estimate of C_(ref) or I_(ref).

Field boundaries are defined in the aerial photos using methods selectedfrom the list comprising: using stored files such as shape files, thatdefine previously established field boundaries to define the currentfield boundaries; using such files from an existing public or privatedatabase; using an automated image analysis routine that uses imagefeatures to identify likely boundaries; and using an image analysisprogram to manually identify the field boundaries using a marking tool.Once the field boundaries are established, image pixels or polygonswithin the field boundaries are selected for analysis, and all otherpixels falling outside the field boundaries are discarded. Manyimage-analysis programs, such as the Environment for Visualization ofImages program (ENVI), possess tools to create image subsets, such as aRegions of Interest (ROI), based on the established field boundarylines.

The presence of bare soil in the aerial image may distort estimates ofcrop health and projected crop yield, so that the pixels correspondingto bare soil may be identified and removed using a number of techniques.A user may visually identify and manually remove the pixelscorresponding to bare soil using existing image-processing software.Alternatively, the elimination of bare soil from the aerial image may beaccomplished by discarding pixels meeting certain criteria, such asgreen/red ratio below a selected value, or normalized differencevegetative index below a selected value, or some other spectral propertythat is useful for distinguishing soil from plants. Suggested criteriafor pixel/polygon removal include a green/red color ratio of less than1.1, or a green/red color ratio that is less than 1.2 times thegreen/red color ratio measured from bare soil in the same image.

Determination of C_(ref) and Calculation of Relative Color (RC)

The reference value of color corresponds to a section of field that isgrowing with ample available nitrogen (C_(ref)). This value is thebenchmark for all color measurements, and all pixel/polygon measurementsof color intensity are expressed relative to the reference value of thecolor selected from blue, red, red-edge, green, infrared, and colorindices calculated from two or more of the preceding. C_(ref) may beestablished by fertilizing a reference area of crop with a high rate ofnitrogen early in the season, recording the area location, andidentifying the area on the corresponding aerial image. C_(ref) may alsobe calculated as the average color value of all pixels or polygonscontained in the reference area. Alternatively, the color values of allpixels or polygons in the one or more fields of interest may be sortedfrom low (dark color) to high (light color), and C_(ref) may becalculated as the mean or median color value of a group of the darkestpixels or polygons. One manifestation of this method is to calculateC_(ref) as the mean or median color value of the darkest 20% (lowestcolor values) of all pixels or polygons, or C_(ref) may be calculated asthe mean or median color value of the pixels or polygons falling in therange between the darkest 10% and the darkest 20% of all pixels orpolygons (lowest color values). Other methods could likely be used aslong as a standard C_(ref) is established.

Thus, for each field, the relative value of color (Relative Color or RC)of each pixel or polygon in the one or more aerial images is calculatedby comparing the color value (C_(i)) of each pixel or polygon toC_(ref). This may be done using division (RC=C_(i)/C_(ref)), subtraction(RC=C_(i)−C_(ref)), or some other method of quantitatively combiningtheir values.

The method described by the present invention is employed to predictcrop yield losses due to nitrogen-deficiency stemming from causes suchas low nitrogen fertilization rate with no mid-season loss of nitrogen(“nitrogen-stress-without-nitrogen-loss”), or sufficient nitrogenfertilization early in the season with subsequent nitrogen loss causedby wet weather or other factors (“nitrogen-loss”).

In an aspect, yield loss (YL), the predicted decrease in cropproductivity (in bushels per acre or other measure of production perunit land area) due to nitrogen deficiency, may be estimated as afunction of Relative Color (to include Relative Index, if used). In thisaspect, the function may be linear or nonlinear.

In one aspect, yield loss may be calculated by substituting the RelativeColor (RC) value or Relative Index (RI) value for each pixel or polygonof the Relative Color or Relative Index map into the linear relation:YL=C ₁×RC−C ₂  Eqn. (1),orYL=C ₁×RI−C ₂  Eqn. (2),

where C₁ is the slope and C₂ is the intercept of a linear fit ofmeasured corn yield data (see Examples 1, 3, 4, and 9), and both C₁ andC₂ assume different values depending on a variety of factors including,but not limited to: the cause of the nitrogen-deficiency, the particularcrop species, the color or colors used to develop the Relative Color orRelative Index Map.

Yield losses may be calculated for the areas represented by pixels, aswell as or for larger areas created by aggregating pixels into polygons,and by aggregating polygons into fields. In the latter case, the yieldloss of each polygon or field may be calculated by substituting theaverage of the RC or RI values of all pixels within the polygon or fieldinto Eqn. 1 or Eqn. 2, or by averaging the yield losses calculated forall pixels in a polygon or field, or all polygons in a field.

Yield losses for each pixel or polygon may be mapped onto the aerialimage by analog (using the same relative locations as thepixels/polygons from the image), or by using paired yield loss andspatial location values. If mapped by analog, total yield loss can becalculated by multiplying average yield loss (previous paragraph) by theknown or measured area of the field. If mapped using spatial locations,average and total yield loss can be calculated using GeographicInformation Systems software. The yield loss map, or alternatively,yield loss average or total for the field, or dollar loss calculated bymultiplying yield loss by grain price, allows the producer to determinethe economic penalty of allowing observed nitrogen deficiencies tocontinue, and balance this against the cost of fertilization. The mapalso, specifically, allows the producer to identify the location of anyrescue nitrogen-fertilizations that may be required.

Determination and Mapping of Economically Optimal Nitrogen FertilizationRate

In the case of sufficient nitrogen fertilization early in the seasonwith subsequent nitrogen loss caused by wet weather or other factors(“nitrogen-loss”), it is unlikely that a reference area for nitrogen hasbeen established by the producer. In this case, the disclosed processallows establishment of the reference color as, for example, the medianof the darkest 20% of the pixels or polygons in the field or acomparable nearby field, as described in more detail above. This allowsaccurate determination of an economically optimal nitrogen rate (EONR)at each point in the field despite the lack of a reference area.Relative Color (RC) can then be calculated as described above, and EONRmay be estimated as a function of Relative Color (to include RelativeIndex, if used). In this aspect, the function may be a linear ornonlinear function that describes a relationship such as the one shownin FIG. 11.

In an aspect where the relationship used to predict EONR takes a linearform, the generalized equation may be EONR=C₃×RC−C₄ (Eqn. 3), where C₃is the slope and C₄ is the intercept of a linear fit of empirical data,using a method similar to the method used to determine the values of C₁and C₂ (see Example 1). The empirical data used to establish the lineartransformation in this aspect were collected from 23 small plotexperiments in farmer fields in Missouri.

In addition, the EONR may be represented spatially, either by analogwith the image, or by combining values with spatial location data foreach pixel or polygon and thus used to construct an EONR map to providea producer or other user with information on an estimated minimum amountof nitrogen fertilizer to use in the midseason application in order tominimize the predicted yield losses and recover the revenue that wouldhave otherwise been lost due to a decrease in overall crop yield. Thus,the precise amount of additional nitrogen fertilizer needed to realizethe maximum potential crop yield may be determined from the EONR map.This guidance may be used generally or by producing a computer file thatcan control a fertilizer applicator to apply the recommended rate ateach point in the field, varying the rate as it crosses the field inresponse to crop color as seen in the aerial image. Other summaryinformation, such as average EONR for the field, total fertilizer needfor the field, and cost estimate for fertilizer plus application mayalso be used to help the producer make a sound decision aboutapplication of additional fertilizer.

The information contained in the yield loss map and the informationcontained in the EONR map may be combined to facilitate the managementof nitrogen fertilizer. The total cost of additional nitrogenfertilization may be easily determined because the exact amount andlocation of fertilizer application is provided. Given additionalinformation about the value of the crop, the economic loss incurred byyield loss if additional nitrogen fertilizer is not provided may also bedetermined. If the potential increase in the value of the harvestexceeds the expense of additional nitrogen fertilization, the producerwould realize a net economic gain by fertilizing. In addition, becausethe information is provided as spatially mapped information, theproducer is provided with the necessary information to perform a similareconomic analysis on subsets or sub-regions of the crop field.

It should be understood from the foregoing that, while particularembodiments have been illustrated and described, various modificationscan be made thereto without departing from the spirit and scope of theinvention as will be apparent to those skilled in the art. Such changesand modifications are within the scope and teachings of this inventionas defined in the claims appended hereto.

EXAMPLES

The following examples illustrate the invention.

Example 1. Development of Method to Estimate Yield Losses from AerialPhotographs

To develop and test a method to estimate corn yield loss due to nitrogendeficiency, the following experiment was conducted. Based on thehypothesis that the areas of cornfields experiencing higher nitrogenloss would appear lighter in aerial photographs and produce loweryields, aerial photographs of seven cornfields that had receivedabove-average May and June rainfall were analyzed as described below.

Selection and characteristics of experimental fields: Seven study fieldswere located in four counties in the northern half of Missouri, spreadover a distance of 270 km, and represented a moderate range ofgeographies, landscape positions, soil genesis factors, and surface soiltextures (see Table 1). All seven fields had uniform fertilizationhistories. All fields were located in regions that received higher-thanaverage precipitation in May and June, and therefore had a highpotential for nitrogen losses due to leaching and denitrificationlosses. The fields used in this experiment were selected based on thedetermination of potential nitrogen deficiency by cooperating producers.

TABLE 1 Information on seven production cornfields photographed in 2001and 2004. Surface Photo Polygon Soil Soil great soil resolution Areasize Polygon Field Year region group texture (m/pixel) (ha) (m²) countAL1 2004 Alluvial Hapludolls* Silty 2.00 41.8 16 13899 clay AL2 2004Alluvial Endoaquerts* Clay 2.00 27.0 16 9686 AL3 2001 AlluvialEndoaquolls* Silty 1.00 2.3 9 1562 clay CP1 2001 Claypan EpiaqualfsSilty 0.54 7.4 10 5421 loam CP2 2001 Claypan Albaqualfs Silty 0.56 6.321 1468 loam CP3 2001 Claypan Epiaqualfs Silty 0.42 8.7 21 2103 loam CP42001 Claypan Epiaqualfs Silty 0.42 5.6 21 1401 loam *All three alluvialfields contained map units representing more than one great group. Theprimary great group was listed and made up between 60% and 70% of thefield area. Secondary great groups, by field, were: AL1, Endoaquerts;AL2, Hapludolls; AL3, Udifluvents.

Aerial photograph acquisition, digitization, and rectification: Aerialphotographic images were acquired from five production cornfields in2001 and two production cornfields in 2004. Aerial photographs in 2001were taken from small-plane flyovers in a nadir (straight down)orientation at altitudes ranging from 1000-1400 m above ground levelusing ASA 400 35 mm color positive film. Larger fields were photographedfrom higher altitudes to fit the whole field onto the camera's field ofview. Photos were obtained on 5 Jul. 2001, and the growth stage of thecorn at that time was approximately V11 to V13. The film was processedinto color slides, and then digitized using a Nikon CoolScan 1.05 filmscanner (Nikon, Inc., Melville, N.Y.). The spatial resolution of thedigitized images ranged from 0.42 to 1.00 m per pixel (see Table 1),depending on differences in the altitudes at which the aerialphotographs were obtained and differences in the focal length used bythe camera to obtain the aerial photographs. Using the Environment forVisualizing Images (ENVI) software version 3.5 (Research Systems, Inc.,Boulder, Colo.), the aerial photos were rectified and formatted to theUniversal Transverse Mercator coordinate system that incorporated theNorth American Datum of 1983 (NAD83), using coordinate points collectedfrom Digital Ortho Quarter Quads produced by the U.S. Geological Surveyand obtained from the map room of the Center for Agricultural, Resource,and Environmental Systems (http://cares.missouri.edu/index.asp).Georeferenced digital aerial photographic images for the two additionalfields, acquired on 24 Jun. 2004 at an estimated corn growth stage ofV10 to V11, were obtained from the National Agricultural Imaging Program(Farm Service Agency, U.S. Dept. of Agriculture). These additionalaerial images had a spatial resolution of 2 m per pixel with 10 m statedaccuracy.

Yield monitor data associated with image data: Maps of corn grain yieldwere obtained from the producers and processed using Spatial ManagementSystem Basic (Ag Leader Technology, Inc., Ames, Iowa). The location ofeach reported corn grain yield was used as the centroid for arectangular polygon in the rectified aerial photographic images.“Closed” blanking (BLN) files, containing the coordinates of thevertices of the closed rectangular polygons, were constructed usingMicrosoft Excel (Microsoft Corp., Redmond, Wash.), imported as textfiles into Surfer 7.0 (Golden Software, Inc., Golden, Colo.), exportedas shapefiles into ENVI 3.5, and used as Regions of Interest in therectified images. The Regions of Interest were used to extract andexport mean digital counts (DCs) for red, green, and blue wavelengths,as well as the associated geographic map coordinates for each polygon.Yield data and mean red, green, and blue DCs for each polygon weremerged using SAS version 8.2 (SAS Institute, Cary, N.C.).

Aerial image processing: Several photographs contained areas of lowvegetative cover, which were removed from the analysis to reduce errorsin the appearance of the crop. All polygons with a green/red pixel colorratio of less than 1.2 were removed from the analysis, using a decisionrule developed using previously acquired photographs of corn fields withhigh resolution (˜4 cm) and low vegetative cover. Using this procedure,no polygons were eliminated from the A3 and CP2 fields. The CP3 and CP4fields had 15% and 55% of the polygons removed, respectively, which werein areas identified by the cooperating corn producer as having severeblack cutworm [Agrotis ipsilon (Hufnagel)] damage. The A1 and A2 fieldshad 17% and 15% of the polygons removed, respectively, mainly in areasidentified by the cooperating corn producer as drainage channels. TheCP1 field had 23% of the polygons removed, mainly at one end of thefield that was identified by producers as suffering substantial standloss due to excess rainfall and subsequent seedling disease.

Aerial Photographic Image Data Processing.

In all fields, reference color, computed independently for red, green,and blue color bands, was defined as the mean value from the darkest 20%of polygons, and represented those areas with sufficient availability ofnitrogen (FIG. 12). Relative color for each polygon was defined eitheras the color value of the polygon (C_(i)) divided by the reference color(C_(ref)) (FIGS. 2-5, 7-9, and 11) or the color of the polygon minus thereference color (FIG. 10).

In order to calculate yield loss, a reference yield value for each fieldwas used to define the potential yield for the field with sufficientnitrogen supply for the plants. Reference yield was defined as theaverage yield for the same polygons (i.e. the darkest 20%) used inestablishing the reference color value. The relative yield for eachpolygon was calculated by dividing each polygon's yield by the referenceyield, and yield loss was calculated by subtracting the reported yieldfor each polygon from the reference yield.

For FIGS. 2-5, polygons in each digitized aerial image were grouped byrelative green value into classes with a constant interval of relativegreen value (<1.00, 1.01 to 1.05, 1.06 to 1.10, 1.11 to 1.15, 1.16 to1.20, etc.). All data associated with each polygon were aggregated intoeach of the classes, and mean values for relative green, relative yield,and yield losses were calculated for each class. Class means forrelative yield and yield loss were regressed against class means forrelative green using SAS software version 8.2 (SAS Institute, Cary,N.C.).

Relationship between aerial photographic data and crop yield: In each ofthe seven study fields, relative yield decreased significantly (P<0.002in each field) as relative green increased, shown in FIG. 2. Thisobservation was consistent with the hypothesis that lighter areas (withhigher green DC and relative green values) had experienced nitrogenloss, which subsequently limited corn yield. The strength of therelationship was related to the degree of nitrogen stress, as assessedby the observed range of either relative green or relative yield.Coefficient of determination ranged from 0.62 in the field with theleast nitrogen stress to >0.9 in the three fields with the most nitrogenstress. Within each relative green class, there was often considerablevariability in relative yield that could be attributed to otherlandscape and management factors. In aggregate, however, thisvariability did not mask the effects of nitrogen on yield potential,suggesting that nitrogen was a major factor limiting yields in thesefields. The relationship between relative green and relative yield wassimilar among all fields, though the CP1 and CP4 fields had steeperslopes than other fields (P=0.011 and 0.0005, respectively, using a testfor equality of slope between individual locations vs. all locationscombined). The observed similarities between fields suggested that ageneral relationship, shown in FIG. 3, could be used to predict relativeyield from future aerial photographs with reasonable accuracy andreliability (r₂=0.79).

Relative greenness was also related to yield loss in each study field,and summarized in FIG. 4 (P<0.002 in each field except CP3, whereP=0.12). As with relative yield, coefficient of determination was lowestin the field with the least nitrogen stress and highest in the fieldswith the most nitrogen stress. The similarity of this relationshipacross fields was even more striking than for the relationship betweenrelative greenness and relative yield. When data from all fields werecombined to form a general relationship, as shown in FIG. 5, thecoefficient of determination was 0.91, which suggested that potentialyield loss can be estimated with good accuracy from aerial photographsfor cases of nitrogen loss.

When data were standardized to reference values for each field andcombined, relative green predicted relative yield with r₂=0.79 and yieldloss with r₂=0.91. Aerial photos provided reasonable predictions ofyield loss due to nitrogen deficiency. These predictions may help cornproducers decide how much expense and trouble is justified in makingrescue nitrogen applications, and additionally may permit large-scaleevaluation of the susceptibility of different nitrogen fertilizermanagement strategies to address nitrogen loss.

Example 2: Aerial Photo Data Used to Manage Nitrogen Supplementation

To demonstrate the feasibility of using aerial photo data to assess crophealth and to determine the appropriate rates of nitrogensupplementation, a demonstration project was established in 2006. Thisproject used data obtained from aerial photos using the methodsdescribed in Example 1 to guide nitrogen fertilizer application througha center-pivot irrigation system, as illustrated in FIG. 6. In thisdemonstration project, the normal pre-planting nitrogen application wasreduced by 50%, and aerial photographs were used to diagnose theadditional nitrogen application rate needed for 150 pivot-irrigatedacres. Based on the fertilization rate determined by the methodsdescribed in Example 1, nitrogen fertilizer use was reduced by 8500 lbof nitrogen (28,000 lb nitrogen fertilizer solution), or 28% of thenormal nitrogen application rate. This recommended nitrogenfertilization rate resulted in a modest 84 bu loss in corn yield, or0.25% of the field's total yield. Results from the south field of thisdemonstration project are shown in FIG. 6.

Example 3: Nitrogen Management Methods Using Aerial Photo Data May beUsed to Manage Nitrogen Fertilization Rates on Experimental Survey Areas

To refine the relationship between aerial photo data and corn yield lossdeveloped using the methods described in Example 1, three experimentalsurvey areas of 1200 to 2000 acres were established in the MissouriRiver bottom of Holt County, Missouri, which received excessive rainfallin April and May 2005. Based on the predictive relationship developed inExample 1, aerial photographs were used to predict an average of 25bu/acre lost yield potential over the survey areas due to nitrogendeficiency. Extrapolated over the whole Missouri River bottom in HoltCounty, this amounted to 1.8 million bushels of lost corn yield in 2005,or about $3.6 million of lost income. Working with community agronomistsand individual producers to collect nitrogen fertilizer managementinformation for these fields, different nitrogen fertilizer sources andmultiple application methods may be compared to determine whichstrategies are most successful at preventing nitrogen loss.

Example 4. Estimating Yield Losses Using Relative Blue Measurements fromAerial Photographs

Using the methods described in Example 1, with the exception thatpolygons were 20-meter squares, and no classes were used, a correlationbetween Yield Loss and Relative Blue values as measured from aerialphotographs of six crop fields was developed. FIG. 7 is a summary of thecorrelation, which had a C1 of 154.01 and a C2 of 153.03. The results ofthis experiment demonstrated the feasibility of estimating Yield Lossusing Relative Blue values as the Relative Color measurement from theaerial photographs of crop field.

Example 5. Estimating Yield Losses Using Relative Red Measurements fromAerial Photographs

Using the methods described in Example 1, with the exception thatpolygons were 20-meter squares, and no classes were used, a correlationbetween Yield Loss and Relative Red values as measured from aerialphotographs of six crop fields was developed. FIG. 8 is a summary of thecorrelation, which had a C1 of 136.24 and a C2 of 136.38. The results ofthis experiment demonstrated the feasibility of estimating Yield Lossusing Relative Red values as the Relative Color measurement from theaerial photographs of crop field.

Using the methods described in Example 1, with the exception thatpolygons were 20-meter squares, no classes were used, and Relative Redwas calculated by subtraction (rather than division as in all otherfigures), a correlation between Yield Loss and Relative Red values asmeasured from aerial photographs of six crop fields was developed. FIG.10 is a summary of the correlation. The results of this experimentdemonstrated the feasibility of using Relative Color values calculatedusing subtraction, while all other figures with graphs demonstrate thefeasibility of using Relative Color values calculated using division.

Example 6. Estimating Yield Losses Using Relative Index Measurementsfrom Aerial Photographs

Using the methods described in Example 1, with the exception thatpolygons were 20-meter squares, no classes were used, and aerial imageand yield map were from a field in north-central Iowa in 2014, acorrelation between Yield Loss and Relative Index values as measuredfrom aerial photographs of crop fields was developed. FIG. 9 is asummary of the correlation, which had a C1 of 146.12 and a C2 of 149.58.In general, for each pixel, the combination index value was calculatedusing the formula: (infrared−green)/(infrared+green). All of thecombination index values were sorted in the field and the median of thedarkest 20% of polygons was set as the reference index value. For eachpixel, the Relative Index value was calculated as RelativeIndex=combination index value for each pixel divided by the referenceindex value. A mathematical relationship was applied, such as the oneshown in the graph of FIG. 9, to predict yield loss. The results of thisexperiment demonstrated the feasibility of estimating Yield Loss usingRelative Index values as the measurement from the aerial photographs ofcrop field.

Example 7. Estimating Economically Optimal Nitrogen Rate Using RelativeColor Measurements from Aerial Photographs

Nitrogen fertilizer rates ranging from 0 to 300 pounds of N per acreswere applied to pre-planned areas in 23 farmer fields. In each field,grain yield associated with each N rate was measured, and EconomicallyOptimal N Rate (EONR) was calculated, that is, the N rate that made themost money. Aerial photographs were acquired 4 times during the growingseason for most of these fields. Reference color for red, green, andblue for each field was set as the average color in aerial photos of allplots at and above the EONR; in most fields, this constituted 20% ormore of the area. For each plot that had received either 0 or 100 poundsN per acre at planting, relative color for red, green, and blue wascalculated by dividing the color intensity for that plot (Ci) by thereference color for that field (Cref). In each field, relative color wasaveraged for all plots receiving 0 N at planting for all three colors;similarly, relative color was averaged for all plots receiving 100pounds N per acre at planting for all three colors. Relative colorvalues and EONR values were grouped across fields by growth stage at thetime the aerial photographs were acquired, using increments of twogrowth stages (that is, V6-V7, V8-V9, V10-V11, V12-V13, V14-V15). Foreach growth stage, EONR values were regressed against relative colorvalues. For most stages and colors, relative color was able to predictEONR. FIG. 11 shows the example of predicting EONR at stages V12-V13using relative green measured in aerial photos.

We claim:
 1. A method for determining a crop yield loss due to nitrogendeficiency in at least one or more crop fields based on an analysis ofat least one or more remote sensing images, the method comprising: a.obtaining the one or more remote sensing images of the one or more cropfields; b. calculating a color value for each pixel of the one or moreremote sensing images or a polygon comprising an aggregation of pixelsof the one or more remote sensing images, wherein the color value is anindividual wavelength or a combination index value comprising at leasttwo wavelengths; c. selecting a reference color value for the field thatrepresents the color value of crop plants with sufficient nitrogen, tobe the same wavelength or combination of wavelengths used in (b); d.calculating a relative color value of each pixel or polygon in the oneor more remote sensing images by quantitatively comparing the colorvalue from that pixel or polygon from (b) to the reference color valuefrom (c); e. estimating a yield loss of each pixel or polygon from itsrelative color value using an empirically determined mathematicalrelationship between the two quantities; and f. presenting a summary ofall yield loss estimates for the field, wherein the yield loss comprisesa decrease in crop yield per land area of a crop.
 2. The method of claim1, wherein the color value and the reference color value arequantitatively compared by division or subtraction to produce therelative color value.
 3. The method of claim 1, wherein the summary ofyield loss is presented visually or numerically with averages, totals,or combinations of the yield loss estimate of each pixel or polygon. 4.The method of claim 3, wherein the summary of yield loss furtherincludes the economic value of such loss.
 5. The method of claim 1,wherein the reference color value is obtained from the darkest areas inthe one or more crop fields being diagnosed or from comparable nearbyfields.
 6. The method of claim 5, wherein the darkest areas are selectedfrom the group consisting of the darkest plants in the field, thedarkest plants in an appropriate neighboring field, measuring the valuein a reference area in which a high rate of nitrogen fertilizer has beenapplied, and combinations thereof.
 7. The method of claim 1, wherein thecrop is selected from the group comprising corn, rice, wheat, potatoes,grass, and cotton.
 8. The method of claim 1, wherein the at least one ormore remote sensing images is a digital image with a resolution rangingbetween about 0.01 meters per pixel and about 30 meters per pixel,wherein the digital image is chosen from aerial photographs, satellitephotographs, photographs obtained by drones, and photographs obtained bytower mounted cameras.
 9. The method of claim 1, further comprising: g.determining a cost of nitrogen fertilization of the crop at arecommended nitrogen application rate and a projected value of the yieldloss of the crop; and h. applying nitrogen fertilizer at the recommendednitrogen application rate if the projected value of the yield loss ofthe crop exceeds the cost of nitrogen fertilization by at least 20%. 10.A method for determining a nitrogen fertilizer rate to alleviate cropnitrogen deficiency in one or more crop fields based on an analysis ofone or more remote sensing images, the method comprising: a. obtainingthe one or more remote sensing images of the one or more crop fields; b.calculating a color value for each pixel of the one or more remotesensing images or a polygon comprising an aggregation of pixels of theone or more remote sensing images, wherein the color value is anindividual wavelength or a combination index value comprising at leasttwo wavelengths; c. selecting a reference color value for the field thatrepresents the color value of crop plants with sufficient nitrogen, tobe the same wavelength or combination of wavelengths used in (b); d.calculating a relative color value of each pixel or polygon in the oneor more remote sensing images by quantitatively comparing the colorvalue from that pixel or polygon from (b) to the reference color valuefrom (c); e. estimating a nitrogen fertilizer rate of each pixel orpolygon from its relative color value using an empirically determinedmathematical relationship between the two quantities; and f. presentinga summary of all nitrogen rate estimates for the field.
 11. The methodof claim 10, wherein the color value and the reference color value arequantitatively compared by division or subtraction to produce therelative color value.
 12. The method of claim 10, wherein the summary ofnitrogen rate estimates is presented visually, as a rate control file,or numerically with averages, totals, or combinations of the nitrogenrate estimate of each pixel or polygon.
 13. The method of claim 12,wherein the summary of nitrogen rate estimates includes a comparison ofthe cost of the suggested nitrogen fertilizer treatment with the cost ofthe yield loss.
 14. The method of claim 10, wherein the reference colorvalue is obtained from the darkest areas in the one or more crop fieldsbeing diagnosed or from comparable nearby fields.
 15. The method ofclaim 14, wherein the darkest areas are selected from the groupconsisting of the darkest plants in the field, the darkest plants in anappropriate neighboring field, measuring the value in a reference areain which a high rate of nitrogen fertilizer has been applied, andcombinations thereof.
 16. The method of claim 10, wherein the crop isselected from the group comprising corn, rice, wheat, potatoes, grass,and cotton.
 17. The method of claim 10, wherein the at least one or moreremote sensing images is a digital image with a resolution rangingbetween about 0.01 meters per pixel and about 30 meters per pixel,wherein the digital image is chosen from aerial photographs, satellitephotographs, photographs obtained by drones, and photographs obtained bytower mounted cameras.
 18. The method of claim 10, further comprising:g. determining a yield loss of the crop; h. determining a cost ofnitrogen fertilization of the crop at the recommended nitrogenfertilizer rate and a projected value of the yield loss of the crop; andi. applying nitrogen fertilizer at the recommended nitrogen fertilizerrate if the projected value of the yield loss of the crop exceeds thecost of nitrogen fertilization by at least 20%.